Paradigm Lock — Universal Identity & Persistence

This paper proves a structural necessity result about identity persistence. Under minimal universal axioms required for identity to be meaningful and non-arbitrary (comparability, drift-bounded persistence, compositional closure, and affine gauge invariance), identity-relevant recurrence is forced to reduce to a single compact 1-DOF trunk, classified as S¹. Given S¹, invariant identity content factors through an SO(2)/O(2) harmonic family {r_k, χ_k}. The paper then proves that identity persistence requires scalar governance and that—up to affine gauge—the unique governance functional compatible with the constraints is PAS_h = Σ w_k r_k (w_k>0), with persistence equivalent to bounded PAS_h drift. No empirical or domain instantiation claims are made in the PROVEN tier.